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Elazar Leibovich
Elazar Leibovich
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Given two positive integers a,b what is the minimal integer n, so that there exist two positive integers u,v for which n=au=av?

It is easy to verify that n=ab/gcd(a,b).

But what happens if instead of requiring au=avau=bv, or |au-av|bv|≤0, we require that |au-av|bv|≤k for some number k?

That is, given two positive integers a,b, what are the minimal integers u,v for which |au-av|bv|≤k, for some k? If there's no direct formula, is there an easy way to find u,v?

Given two positive integers a,b what is the minimal integer n, so that there exist two positive integers u,v for which n=au=av?

It is easy to verify that n=ab/gcd(a,b).

But what happens if instead of requiring au=av, or |au-av|≤0, we require that |au-av|≤k for some number k?

That is, given two positive integers a,b, what are the minimal integers u,v for which |au-av|≤k, for some k? If there's no direct formula, is there an easy way to find u,v?

Given two positive integers a,b what is the minimal integer n, so that there exist two positive integers u,v for which n=au=av?

It is easy to verify that n=ab/gcd(a,b).

But what happens if instead of requiring au=bv, or |au-bv|≤0, we require that |au-bv|≤k for some number k?

That is, given two positive integers a,b, what are the minimal integers u,v for which |au-bv|≤k, for some k? If there's no direct formula, is there an easy way to find u,v?

Post Closed as "too localized" by Kim Morrison
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Elazar Leibovich
Elazar Leibovich
  • 123
  • 5

For which integers u,v does au=bv *approximately*?

Given two positive integers a,b what is the minimal integer n, so that there exist two positive integers u,v for which n=au=av?

It is easy to verify that n=ab/gcd(a,b).

But what happens if instead of requiring au=av, or |au-av|≤0, we require that |au-av|≤k for some number k?

That is, given two positive integers a,b, what are the minimal integers u,v for which |au-av|≤k, for some k? If there's no direct formula, is there an easy way to find u,v?